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CAT 2025 Lesson : Quant: Jan '25 to Feb '25 - Numbers 2 Solving - 11 Jan 2025
Numbers 2
1) A number leaves a remainder of 10 when divided by 18. What is the remainder when the same number is divided by 3?
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2) What is the sum of the remainders we get when 4735781 is divided by each of 2, 3, 4, 5, 8 and 9?
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3) What is the product of the remainders we get when 8657925 is divided by each of 7, 11, 13, 19, 20 and 25?
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4) What is the largest possible number that divides 37, 75 and 115 with remainders of 1, 3 and 7 respectively?
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5) How many different positive integers would divide 37, 85 and 109 and leave the same remainder?
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6) What is the second smallest positive integer which would leave a remainder of 3 when divided by 5, 6 or 8?
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7) What is the fourth smallest positive integer which, when successively divided by 3, 5 and 6, would leave remainders of 1, 3 and 4 respectively?
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8) What is the remainder when (3748 + 2779) (5865 - 4871) is divided by 9?
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9) Find the remainder when 5 is divided by 6.
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10) What is the remainder when 275 is divided by 29?
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11) What is the largest power of 135 that perfectly divides 200!?
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12) What is the last digit of (43 17) - (56 + 48)?
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13) What are the last 2 digits of 239?
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14) How many different ordered pairs () exist such that where and are integers?
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15) In how many ways can 450 be written as the sum of 2 or more consecutive natural numbers?
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16) . What is the remainder when a is divided by ?
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17) How many consecutive zeroes are there at the end (i.e. right-most end) of the integer ?
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18) How many consecutive zeroes are there at the end (i.e. right-most end) of 400!?
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19) What are the last two digits of ?
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20) Where is a natural number, which of the following can never be the number of consecutive zeroes at the right-most end of !?
(1) 26
(2) 28
(3) 29
(4) 31
1) A number leaves a remainder of 10 when divided by 18. What is the remainder when the same number is divided by 3?
Answer:
2) What is the sum of the remainders we get when 4735781 is divided by each of 2, 3, 4, 5, 8 and 9?
Answer:
3) What is the product of the remainders we get when 8657925 is divided by each of 7, 11, 13, 19, 20 and 25?
Answer:
4) What is the largest possible number that divides 37, 75 and 115 with remainders of 1, 3 and 7 respectively?
Answer:
5) How many different positive integers would divide 37, 85 and 109 and leave the same remainder?
Answer:
6) What is the second smallest positive integer which would leave a remainder of 3 when divided by 5, 6 or 8?
Answer:
7) What is the fourth smallest positive integer which, when successively divided by 3, 5 and 6, would leave remainders of 1, 3 and 4 respectively?
Answer:
8) What is the remainder when (3748 + 2779) (5865 - 4871) is divided by 9?
Answer:
9) Find the remainder when 5 is divided by 6.
Answer:
10) What is the remainder when 275 is divided by 29?
Answer:
11) What is the largest power of 135 that perfectly divides 200!?
Answer:
12) What is the last digit of (43 17) - (56 + 48)?
Answer:
13) What are the last 2 digits of 239?
Answer:
14) How many different ordered pairs () exist such that where and are integers?
Answer:
15) In how many ways can 450 be written as the sum of 2 or more consecutive natural numbers?
Answer:
16) . What is the remainder when a is divided by ?
Answer:
17) How many consecutive zeroes are there at the end (i.e. right-most end) of the integer ?
Answer:
18) How many consecutive zeroes are there at the end (i.e. right-most end) of 400!?
Answer:
19) What are the last two digits of ?
Answer:
20) Where is a natural number, which of the following can never be the number of consecutive zeroes at the right-most end of !?
(1) 26
(2) 28
(3) 29
(4) 31
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